All four designs do the same thing: they direct water at a place you would otherwise rub dry. They differ only in how much bathroom they need for it.
The classic bidet is a ceramic basin of its own with its own plumbing, roughly 70 by 40 centimeters, usually beside the toilet. You sit on it. That is the design the name belongs to – and the one that no longer fits into a standard German bathroom.
The shower toilet is a toilet with a built-in nozzle. One piece of ceramic instead of two, but with machinery inside and a price that belongs to a bathroom renovation rather than a shopping trip.
The bidet seat goes under the toilet seat or replaces it entirely, depending on the type. The nozzle extends when needed, and the water comes from the angle valve next to the toilet or from the washbasin. No new pipe, no new ceramic.
The portable butt shower is a bottle with a nozzle that you fill yourself. It needs nothing at all – no valve, no hose, no fixed toilet.
Why it stayed rare here: German bathrooms are often small, and a bidet costs a square meter. Where space is tight, the basin you consider dispensable is the one that goes. The water was never the problem; the second basin was. That is exactly why the three retrofit designs exist.